Following meeting with Ilan
Jonathan Harrison
9 October 2018
Notes following meeting with Ilan on 8th October.
Include observed data in Figure 7 or similar figure. Show unnormalised. Also quantify in WT and OE the number and fraction of transcripts that are localized. Demonstrate that particles are equivalent between WT and the OE mutant.
To investigate: Inhomogeneous production due to patchy expression of the gal-4 driver. Inhomogeneous transport through ring canals. Waiting of mRNA to form into complexes at the nuclear pore complex, such as for assembly with dynein or other proteins. (Model comparison between some of these are the ‘normal’ model).
Observed data
Observed distribution of RNA across cells
To illustrate these ideas, we plot the RNA distributions for WT and OE based on observed data. 
The same thing but without the normalisation:
Show the number and fraction of complexes localized
These plots of the observed data suggest that the fraction of complexes localized is different between wild type and overexpressor. The number of transcripts localized also appeasrs lower in the overexpression mutant, but in my opinion this is due to the age/size of the egg chambers considered. The egg chambers quantified are generally smaller. (Possible bias here as there are too many particles in the larger overexpression datasets so that MATLAB runs out of memory in running the FISH-quant code to localize the transcripts.)
How many times greater is production in the overexpressor than in wild type?
We fit a linear model to the data on total RNA counts in each egg chamber for each phenotype. If \[z = \sum_{i=1}^{16} y_i\] is the total RNA count in each egg chamber, then \[\frac{\text{d} z}{\text{d} t} = 15a.\] Therefore \[ z = z_0 + 15at.\]
Based on the total RNA counts in each egg chamber, we can estimate production rate \(a\) directly for WT and OE data and give a ratio of how much bigger the production for the OE is.
## [1] 9.714501## [1] 24.57184## [1] 2.529398This neglects effects from assembly in the oocyte, which we ought to account for.
## [1] 17.74595## [1] 32.81549## [1] 1.849182Based on this it seems reasonable to keep using \(2a\) as the production in the overexpressor.
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [2,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [3,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [4,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [5,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [6,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [7,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [8,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [9,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [,14] [,15] [,16]
## [1,] 2 2 2
## [2,] 2 2 2
## [3,] 2 2 2
## [4,] 2 2 2
## [5,] 2 2 2
## [6,] 2 2 2
## [7,] 2 2 2
## [8,] 2 2 2
## [9,] 2 2 2
## [,1] [,2] [,3]
## [1,] 1 1 1
## [2,] 1 1 1
## [3,] 1 1 1
## [4,] 1 1 1
## [5,] 1 1 1
## [6,] 1 1 1
## [7,] 1 1 1
## [8,] 1 1 1
## [9,] 1 1 1
##
## Computed from 4000 by 9 log-likelihood matrix
##
## Estimate SE
## elpd_loo -6719.1 5505.6
## p_loo 766.9 624.1
## looic 13438.3 11011.2
## ------
## Monte Carlo SE of elpd_loo is NA.
##
## Pareto k diagnostic values:
## Count Pct. Min. n_eff
## (-Inf, 0.5] (good) 1 11.1% 788
## (0.5, 0.7] (ok) 1 11.1% 354
## (0.7, 1] (bad) 1 11.1% 171
## (1, Inf) (very bad) 6 66.7% 1
## See help('pareto-k-diagnostic') for details.
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [2,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [3,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [4,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [5,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [6,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [7,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [8,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [9,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [,14] [,15] [,16]
## [1,] 2 2 2
## [2,] 2 2 2
## [3,] 2 2 2
## [4,] 2 2 2
## [5,] 2 2 2
## [6,] 2 2 2
## [7,] 2 2 2
## [8,] 2 2 2
## [9,] 2 2 2
## [,1] [,2] [,3]
## [1,] 6 9 1
## [2,] 16 1 1
## [3,] 12 16 1
## [4,] 10 11 1
## [5,] 16 1 1
## [6,] 10 1 1
## [7,] 1 1 1
## [8,] 6 11 16
## [9,] 6 11 1
##
## Computed from 4000 by 9 log-likelihood matrix
##
## Estimate SE
## elpd_loo -6670.7 5497.0
## p_loo 758.8 644.3
## looic 13341.4 10994.0
## ------
## Monte Carlo SE of elpd_loo is NA.
##
## Pareto k diagnostic values:
## Count Pct. Min. n_eff
## (-Inf, 0.5] (good) 1 11.1% 774
## (0.5, 0.7] (ok) 2 22.2% 283
## (0.7, 1] (bad) 1 11.1% 15
## (1, Inf) (very bad) 5 55.6% 1
## See help('pareto-k-diagnostic') for details.
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [2,] 0 2 2 4 2 4 4 4 2 4 4 4 4
## [3,] 0 2 2 4 2 2 4 4 2 2 4 4 2
## [4,] 0 4 2 4 2 4 2 2 2 2 2 4 4
## [5,] 0 2 2 2 2 2 4 2 2 2 4 2 2
## [6,] 0 2 2 4 2 2 4 4 2 4 4 4 4
## [7,] 0 2 2 4 2 4 4 4 2 4 4 2 4
## [8,] 0 2 2 4 2 2 4 4 2 2 4 4 4
## [9,] 0 2 2 4 2 2 4 4 2 2 4 4 4
## [,14] [,15] [,16]
## [1,] 2 2 2
## [2,] 4 4 4
## [3,] 2 4 4
## [4,] 2 4 4
## [5,] 2 2 2
## [6,] 2 4 4
## [7,] 4 4 4
## [8,] 2 4 4
## [9,] 2 4 4
## [,1] [,2] [,3]
## [1,] 1 1 1
## [2,] 1 1 1
## [3,] 1 1 1
## [4,] 1 1 1
## [5,] 1 1 1
## [6,] 1 1 1
## [7,] 1 1 1
## [8,] 1 1 1
## [9,] 1 1 1
##
## Computed from 4000 by 9 log-likelihood matrix
##
## Estimate SE
## elpd_loo -7116.7 5817.1
## p_loo 983.3 766.9
## looic 14233.4 11634.3
## ------
## Monte Carlo SE of elpd_loo is NA.
##
## Pareto k diagnostic values:
## Count Pct. Min. n_eff
## (-Inf, 0.5] (good) 1 11.1% 850
## (0.5, 0.7] (ok) 0 0.0% <NA>
## (0.7, 1] (bad) 1 11.1% 46
## (1, Inf) (very bad) 7 77.8% 1
## See help('pareto-k-diagnostic') for details.
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## [1,] 0 2 2 2 2 2 2 2 2 2 2 2 2
## [2,] 0 2 2 4 2 4 4 4 2 4 4 4 4
## [3,] 0 2 2 4 2 2 4 4 2 2 4 4 2
## [4,] 0 4 2 4 2 4 2 2 2 2 2 4 4
## [5,] 0 2 2 2 2 2 4 2 2 2 4 2 2
## [6,] 0 2 2 4 2 2 4 4 2 4 4 4 4
## [7,] 0 2 2 4 2 4 4 4 2 4 4 2 4
## [8,] 0 2 2 4 2 2 4 4 2 2 4 4 4
## [9,] 0 2 2 4 2 2 4 4 2 2 4 4 4
## [,14] [,15] [,16]
## [1,] 2 2 2
## [2,] 4 4 4
## [3,] 2 4 4
## [4,] 2 4 4
## [5,] 2 2 2
## [6,] 2 4 4
## [7,] 4 4 4
## [8,] 2 4 4
## [9,] 2 4 4
## [,1] [,2] [,3]
## [1,] 1 1 1
## [2,] 1 1 1
## [3,] 1 1 1
## [4,] 1 1 1
## [5,] 1 1 1
## [6,] 1 1 1
## [7,] 1 1 1
## [8,] 1 1 1
## [9,] 1 1 1
##
## Computed from 4000 by 9 log-likelihood matrix
##
## Estimate SE
## elpd_loo -6596.8 5534.3
## p_loo 780.0 727.8
## looic 13193.5 11068.5
## ------
## Monte Carlo SE of elpd_loo is NA.
##
## Pareto k diagnostic values:
## Count Pct. Min. n_eff
## (-Inf, 0.5] (good) 3 33.3% 294
## (0.5, 0.7] (ok) 0 0.0% <NA>
## (0.7, 1] (bad) 2 22.2% 199
## (1, Inf) (very bad) 4 44.4% 1
## See help('pareto-k-diagnostic') for details.
## elpd_diff se
## 48.4 19.7## elpd_diff se
## -397.6 314.1## elpd_diff se
## -446.0 323.5## elpd_diff elpd_loo se_elpd_loo p_loo se_p_loo looic
## res_prod4a[[2]] 0.0 -6596.8 5534.3 780.0 727.8 13193.5
## res_block[[2]] -73.9 -6670.7 5497.0 758.8 644.3 13341.4
## res_simple[[2]] -122.4 -6719.1 5505.6 766.9 624.1 13438.3
## res_prod[[2]] -519.9 -7116.7 5817.1 983.3 766.9 14233.4
## se_looic
## res_prod4a[[2]] 11068.5
## res_block[[2]] 10994.0
## res_simple[[2]] 11011.2
## res_prod[[2]] 11634.3